In modern astronomy, an important activity is the search for exoplanets. An exoplanet is a planet in orbit around a star other than the sun. A difficulty encountered in the exoplanet discovery effort is the fact that the star is significantly brighter and larger in size than any exoplanet in orbit around the star. Indirect methods have been utilized to find exoplanets, such as efforts to detect a gravitational effect of the exoplanet on the host star, and changes in luminosity of the host star as a result of the passing of the exoplanet in front of the star.
Once an exoplanet is discovered, it would be advantageous to study the composition of the exoplanet. Spectroscopy is a known scientific tool used for the study of the composition of celestial objects. Spectroscopy analyzes the spectrum of light received from a celestial object to identify the composition. However, an artifact of imaging devices is a broad blurry smudge or “halo” effect around a bright object, such as a star. The halo obscures extremely faint objects next to the star, such as exoplanets, preventing spectral analysis of light from the exoplanet.
A halo effect is symptomatic of astrophysical studies, which rely upon precision measurements of the distribution of light from celestial objects that are typically hampered by strong disturbances to the received light due to the turbulent atmosphere of the earth, as well as by imperfections in the optics of the telescope. A diffraction-limited image refers to a best form of image obtainable using a particular telescope, at a specific location.
A perfect diffraction-limited image is one that is immune to the effects of the atmosphere, optical manufacturing errors or any other source of imaging errors. For years, adaptive optics and space-borne telescopes have achieved diffraction-limited images of varying levels of perfection. The enormous power of diffraction-limited imaging is clear when reference is made to the profound impact that the Hubble Space Telescope, situated above Earth's atmosphere, has had on nearly every field of astronomy. Ground-based adaptive optical systems that form diffraction-limited images, by correcting the deleterious effects of the atmosphere, have facilitated discovery of many types of phenomena as well, including, for example, brown dwarfs, objects intermediate in mass between planets and stars.
A widely used metric for quantifying the level of perfection of an image is the Strehl ratio, S, which is the peak intensity of the observed image of an unresolved or point source divided by the theoretically perfect peak intensity, in which no errors in the wave front are present. When the wave front errors are small, S=e−σ sup 2, where σ is the standard deviation of the wave front error (the Marechal approximation) and “σ sup 2” is σ2 (σsquared). A value of 1.00 or 100% indicates a perfect diffraction-limited image. Images without adaptive optics typically have S˜0.5% on telescopes larger than about 1 m. The best ground and space-based images achieve S˜80 to 90% in the optical and near infrared wavelengths (0.5 to 3 μm).
As a consequence of the finite size of a telescope, there is diffraction that spreads the light into an Airy-pattern distribution at the image plane formed by the telescope, if it has an un-obscured, circular entrance pupil. 84% of the energy from each point source in such diffraction-limited images is constrained to a tiny spot of diameter 2.44θDL, where θDL=λ/D, θDL is the diffraction-limited image resolution, λ is the wavelength of light used in the observation and D is the telescope diameter. For reference, θDL is 125 nanoradians or 25.8 milliarcseconds (mas) for an 8-m telescope used at a wavelength of 1.0 μm.
In diffraction-limited images, light that is not constrained to the perfect optical diffraction pattern, 1−S, is scattered into a broad blurry smudge that forms the halo effect around each point source of light in the image. As noted, the halo drowns out faint objects that may be next to bright ones. Removing this obscuring halo of light, which is only an artifact of the imaging device and medium through which the light traveled, and not astrophysical in nature, would permit the study of extremely faint objects next to bright stars, such as exoplanets. Indeed, as an example, if the solar system were observed from the vantage of 30 light years distant, Earth would be only 100 mas (4θDL for the 8-m telescope) from the Sun and about 1010 times fainter, thus, completely obscured by the halo of light from the Sun's image in a current telescope. The full width of this halo measured at half the maximum value can be larger than 1 arcsecond, in the case of poorly corrected images made at wavelengths of around 1 μm.